Communications networks employ satellites operating in geosynchronous orbits in combination with terrestrial facilities such as land lines, microwave repeaters, and undersea cables to provide communications over vast areas of the earth. Geosynchronous satellites and terrestrial facilities are both expensive to install and to maintain and thus are not a cost effective means of increasing network capacity. In addition, geosynchronous satellites which operate at an altitude of 22,300 miles above the earth are unsuitable for supporting cellular service because of the extremely high power levels that would be required to communicate with satellites at that altitude.
More recently, constellations of low earth orbit (LEO) satellites have been proposed and are being developed as a cost effective means for providing increased capacity and supporting cellular and broadband data service for communications networks. In such a constellation, the satellites are divided into a number of orbital planes. Because low earth orbit satellites move rapidly with respect to the earth, each orbital plane includes a number of satellites that maintain continuous coverage for underlying cells defined on the surface of the earth. A footprint of cells represent the coverage region for each satellite.
Low earth orbit satellites utilize antennas which form a cluster of beams each assigned a ground-based cell. Due to the geometry of low earth satellites above the spherical surface of the earth, cells near the edges of the footprint have a much smaller angular size and closer angular spacing than cells near the center of the footprint. To accurately process signals from the cells, the antenna shapes each beam to match the angular size of its assigned cell. Existing beam shaping systems utilize phase shifting devices that greatly increase the complexity of the antenna and thus the cost of the satellite.